I thought of the Sonata III 500
(it's out of stock at newegg but available elsewhere), BUT! I wouldn't recommend it.
And here's the conundrum: Some of your restrictions on a case negatively impact the temperature in the case. Case in point, the Sonata III has a door, doesn't have fan openings on the top or the side - it actually only has one place for a fan in the rear (and this location could accommodate most closed-loop CPU coolers). Unfortunately, with all the other components you're rockin' (the 780 and the i7 CPU), the case design inhibits necessary airflow needed which could lead to high thermals and an unstable system.
Please keep that in mind when you ultimately select a case. And let us know what you pick.
Hope this helps.